Near viability for fully nonlinear differential inclusions |
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Authors: | Irina Căpraru Alina I. Lazu |
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Affiliation: | 1. Department of Mathematics, “Al. I. Cuza” University of Ia?i, Bd. Carol I, no. 11, Ia?i, 700506, Romania 2. Department of Mathematics, “Gh. Asachi” Technical University, Ia?i, 700506, Romania
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Abstract: | We consider the nonlinear differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A is an m-dissipative operator on a separable Banach space X and F is a multi-function. We establish a viability result under Lipschitz hypothesis on F, that consists in proving the existence of solutions of the differential inclusion above, starting from a given set, which remain arbitrarily close to that set, if a tangency condition holds. To this end, we establish a kind of set-valued Gronwall’s lemma and a compactness theorem, which are extensions to the nonlinear case of similar results for semilinear differential inclusions. As an application, we give an approximate null controllability result. |
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